
Forbidden top decays, such as \(t\rightarrow q\tau \ell \)  with \(q=c,u\)  and \(\ell =\mu ,e\) . There are currently no upper bounds on these decay rates [1]}.

Forbidden tau decays, for two of which there are experimental upper bounds [2]}, [3]}:
\({\cal B}(\tau \rightarrow \mu \pi ^0)&<&1.1\times 10^{-7},\numero \\{\cal B}(\tau \rightarrow e\pi ^0)&<&8.0\times 10^{-8}.\) 
Compared to the allowed \(\tau \rightarrow \nu _\tau \bar{u}q\ (q=d,s)\) , with \({\cal B}(\tau \rightarrow \nu \bar{u}q)\sim 0.65\) , there is a CKM suppression of \(|V_{ub}V_{us}|^2\sim 7\times 10^{-7}\) . Thus, branching ratios of \({\cal O}(10^{-7})\)  do not provide significant bounds.

Allowed \(\tau \)  decays: The ratio \({\cal B}(\tau \rightarrow K\nu )/{\cal B}(\tau \rightarrow \pi \nu )\)  is modified because the contribution is only to the former. Both branching ratios are measured, with [1]}
\(R_{K/\pi }\equiv \Gamma (K^-\nu )/\Gamma (\pi ^-\nu )=(6.44\pm 0.09)\times 10^{-2}.\) 
The SM gives [5]}
\(R_{K/\pi }=\frac{f_K^2|V_{us}|^2}{f_\pi ^2|V_{ud}|^2}\frac{(1-m_K^2/m_\tau ^2)^2}{(1-m_\pi ^2/m_\tau ^2)^2}(1+\delta _{\rm LD}),\) 
where \(\delta _{\rm LD}=(0.03\pm 0.44)\%\)  is the long distance correction, and \(f_K/f_\pi =1.189\pm 0.007\) . The new contribution to \(\tau \rightarrow K\nu \)  is CKM suppressed by \(|V_{ub}/V_{us}|^2\sim 3\times 10^{-4}\)  compared to the SM contribution, and so it is well below the uncertainty from \(\delta _{\rm LD}\)  and cannot be constrained.

Forbidden \(J/\psi \)  decays [6]}, [7]}:
\({\cal B}(J/\psi \rightarrow \mu ^\pm \tau ^\mp )&<&2.0\times 10^{-6},\numero \\{\cal B}(J/\psi \rightarrow e^\pm \tau ^\mp )&<&7.5\times 10^{-8}.\) 
Compared to the allowed \(J/\psi \rightarrow \ell ^+\ell ^-\) , with \({\cal B}(J/\psi \rightarrow \ell ^+\ell ^-)\sim 0.06\) , there is a CKM suppression \(|V_{cb}V_{cs}|^2\sim 1.6\times 10^{-3}\) . Furthermore [8]}, [9]},
\(\frac{{\cal B}(J/\psi \rightarrow \tau ^\pm \ell ^\mp )}{{\cal B}(J/\psi \rightarrow \ell ^+\ell ^-)}\propto \left(\frac{m_{J/\psi }}{\Lambda }\right)^4.\) 
Thus, the bound on \(\Lambda /\sqrt{|C_3^e|}\)  is of \({\cal O}(6m_{J/\psi })\)  and on \(\Lambda /\sqrt{|C_3^\mu |}\)  even weaker.

